# Distribution functions of linear combinations of lattice polynomials from the uniform distribution

@article{Marichal2007DistributionFO, title={Distribution functions of linear combinations of lattice polynomials from the uniform distribution}, author={Jean-Luc Marichal and Ivan Kojadinovic}, journal={arXiv: Probability}, year={2007} }

We give the distribution functions, the expected values, and the moments of linear combinations of lattice polynomials from the uniform distribution. Linear combinations of lattice polynomials, which include weighted sums, linear combinations of order statistics, and lattice polynomials, are actually those continuous functions that reduce to linear functions on each simplex of the standard triangulation of the unit cube. They are mainly used in aggregation theory, combinatorial optimization…

## Figures from this paper

## 6 Citations

On the moments and distribution of discrete Choquet integrals from continuous distributions

- Mathematics
- 2009

We study the moments and the distribution of the discrete Choquet integral when regarded as a real function of a random sample drawn from a continuous distribution. Since the discrete Choquet…

On the Moments and the Distribution of the Choquet Integral

- Mathematics, Computer ScienceEUSFLAT Conf.
- 2007

We investigate the distribution functions and the moments of the so-called Choquet integral, also known as the Lovasz extension, when regarded as a real function of a random sample drawn from a…

Type-I hybrid censoring of uniformly distributed lifetimes

- Mathematics
- 2019

ABSTRACT We consider Type-I hybrid censored lifetimes from a two-parameter uniform distribution with support [a, b] and focus on the derivation of the exact distribution of the MLEs. In particular,…

Behavioral analysis of aggregation functions

- Mathematics
- 2009

Aggregation functions arise wherever aggregating information is important: applied and pure mathematics (probability, statistics, decision theory, functional equations), operations research, computer…

## References

SHOWING 1-10 OF 27 REFERENCES

The exact and approximate distributions of linear combinations of selected order statistics from a uniform distribution

- Mathematics
- 1985

SummaryThe exact probability density function is given for linear combinations ofk=k(n) order statistics selected from whole order statistics based on random sample of sizen drawn from a uniform…

Cumulative distribution functions and moments of lattice polynomials

- Mathematics
- 2006

We give the cumulative distribution functions, the expected values, and the moments of lattice polynomials when regarded as real functions. Since lattice polynomial functions include order…

Extensions of functions of 0-1 variables and applications to combinatorial optimization

- Mathematics
- 1985

For in § 2 we introduce and study “tight extensions” fD : [0, 1]n → R, defined on each n-simplex Di of a triangulation D of [0,1]n, with all vertices in {0,1}n, as the unique affine function which…

LINEAR FUNCTIONS OF UNIFORM ORDER STATISTICS AND B-SPLINES

- Mathematics
- 2002

ABSTRACT The purpose of the present paper is to give a simplified method of finding the density function and the moments of linear function of order statistics from uniform distribution. This is done…

Constructive Approximation

- Computer ScienceGrundlehren der mathematischen Wissenschaften
- 1993

This paper works on [-1, 1 ] and obtains Markov-type estimates for the derivatives of polynomials from a rather wide family of classes of constrained polynomes and results turn out to be sharp.

Submodular functions and convexity

- Mathematics, Computer ScienceISMP
- 1982

In “continuous” optimization convex functions play a central role, and linear programming may be viewed as the optimization of very special (linear) objective functions over very special convex domains (polyhedra).

Slices, Slabs, and Sections of the Unit Hypercube

- Mathematics
- 2006

Using combinatorial methods, we derive several formulas for the volume of convex bodies obtained by intersecting a unit hypercube with a halfspace, or with a hyperplane of codimension 1, or with a…

Approximation theory and methods

- Mathematics
- 1981

Preface 1. The approximation problem and existence of best approximations 2. The uniqueness of best approximations 3. Approximation operators and some approximating functions 4. Polynomial…

Error bounds in divided difference expansions. A probabilistic perspective

- Mathematics
- 2006

We give error bounds for the remainder term, as well as sharp upper and lower bounds for the leading term, in divided difference expansions. A main feature of this paper is the use of a probabilistic…

Aggregation of interacting criteria by means of the discrete Choquet integral

- Mathematics
- 2002

The most often used operator to aggregate criteria in decision making problems is the classical weighted arithmetic mean. In many problems however, the criteria considered interact, and a substitute…